
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd


# We open the data 
df = pd.read_csv('Nikkei-2010-2012.csv',index_col="Ticker")
df


# We use numpy to create the correlation matrix

#First convert the data into an array
mat = np.array(df.T[1::],float)
print(mat)
# Correlation:
C= np.corrcoef(mat.T)
C

[[ 999. 3850.  694. ... 2119. 1865. 1580.]
 [ 989. 3870.  700. ... 2123. 1880. 1615.]
 [1003. 3870.  700. ... 2123. 1870. 1625.]
 ...
 [ 850. 3865.  798. ...  967. 2025. 1595.]
 [ 851. 3860.  780. ...  952. 2010. 1580.]
 [ 849. 3855.  775. ...  907. 1975. 1570.]]

array([[ 1.        ,  0.09219277,  0.2779862 , ...,  0.09768973,
         0.25497464,  0.41110819],
       [ 0.09219277,  1.        ,  0.03848122, ...,  0.68840317,
         0.25415725,  0.22398847],
       [ 0.2779862 ,  0.03848122,  1.        , ..., -0.56446518,
         0.68886603,  0.63470219],
       ...,
       [ 0.09768973,  0.68840317, -0.56446518, ...,  1.        ,
        -0.18973217, -0.17148206],
       [ 0.25497464,  0.25415725,  0.68886603, ..., -0.18973217,
         1.        ,  0.85186864],
       [ 0.41110819,  0.22398847,  0.63470219, ..., -0.17148206,
         0.85186864,  1.        ]])


# Now we plot the heat map of this matrix

plt.imshow(C)
plt.colorbar()
plt.show()


eig = np.linalg.eigvals(C)
eig_nonzero = [i for i in eig if abs(i) > 0.001]
a,b,c = plt.hist(eig_nonzero, density = True,range = [0,1], bins = 100)


### First we will compute the returns matrix
# We define the function "returns"

#This function takes as input a matrix where each rhow is a time series
def returns(mat):
    # T is the number of columns, that is, the number of times measured
    T = len(mat[0])
    
    #We define a new matrix, which will be the matrix of returns. It has one less column because
    # of the definition of returns
    new_mat = np.zeros((len(mat),T-1))
    
    #Iterate over every column
    for i in range(T-1):
        #We define the new column with the definition of the returns. 
        new_mat.T[i] = (mat.T[i+1]-mat.T[i])/mat.T[i]
    
    return(new_mat)

mat = np.array(df.T[1::].T,float)
print(mat)
print(np.around(returns(mat),5))
#It seems to be correct.

[[ 999.  989. 1003. ...  850.  851.  849.]
 [3850. 3870. 3870. ... 3865. 3860. 3855.]
 [ 694.  700.  700. ...  798.  780.  775.]
 ...
 [2119. 2123. 2123. ...  967.  952.  907.]
 [1865. 1880. 1870. ... 2025. 2010. 1975.]
 [1580. 1615. 1625. ... 1595. 1580. 1570.]]
[[-0.01001  0.01416 -0.01894 ... -0.00701  0.00118 -0.00235]
 [ 0.00519  0.       0.0155  ...  0.      -0.00129 -0.0013 ]
 [ 0.00865  0.       0.      ...  0.00125 -0.02256 -0.00641]
 ...
 [ 0.00189  0.      -0.00094 ... -0.01024 -0.01551 -0.04727]
 [ 0.00804 -0.00532  0.00802 ... -0.00246 -0.00741 -0.01741]
 [ 0.02215  0.00619  0.00308 ...  0.      -0.0094  -0.00633]]


# Compute the correlation matrix for the return matrix
mat_ret = returns(mat)
C= np.corrcoef(mat_ret)
C

plt.imshow(C,vmin=-1,vmax=1)
plt.colorbar()
plt.show()


#The eigenvalues of this matrix
eig = np.linalg.eigvals(C)
eig_nonzero = [i for i in eig if abs(i) > 0.001]
a,b,c = plt.hist(eig_nonzero, density = True,range = [0,1], bins = 100)


epochs = []

# Number of epochs
N = df.shape[1]//40
N

for i in range(N):
    #Take the ith epoch
    ep = df.iloc[:,1 + i*40:1+(i+1)*40]
    epochs.append(ep)


# Plot the heatmap and eigenvalues of each epoch.

for i in range(N):
    ep = epochs[i]
    mat = np.array(ep)
    print(mat)
    
    print("epoch number: ", i)
    
    C= np.corrcoef(mat)
    
    print("Correlation matrix")
    plt.imshow(C)
    plt.colorbar()
    plt.show()
    
    
    print("Eigenvalues:")
    
    eig = np.linalg.eigvals(C)
    eig_nonzero = [i for i in eig if abs(i) > 0.001]
    a,b,c = plt.hist(eig_nonzero, density = True, bins = 100)
    plt.show()

[[ 999.  989. 1003. ...  921.  937.  961.]
 [3850. 3870. 3870. ... 4025. 4015. 4035.]
 [ 694.  700.  700. ...  669.  669.  655.]
 ...
 [2119. 2123. 2123. ... 2104. 2121. 2135.]
 [1865. 1880. 1870. ... 1935. 1965. 1985.]
 [1580. 1615. 1625. ... 1610. 1645. 1660.]]
epoch number:  0
Correlation matrix

Eigenvalues:

C:\ProgramData\Anaconda3\lib\site-packages\numpy\lib\histograms.py:851: ComplexWarning: Casting complex values to real discards the imaginary part
  indices = f_indices.astype(np.intp)
C:\ProgramData\Anaconda3\lib\site-packages\numpy\lib\histograms.py:904: ComplexWarning: Casting complex values to real discards the imaginary part
  db = np.array(np.diff(bin_edges), float)
C:\ProgramData\Anaconda3\lib\site-packages\numpy\core\_asarray.py:102: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)
C:\ProgramData\Anaconda3\lib\site-packages\matplotlib\transforms.py:1966: ComplexWarning: Casting complex values to real discards the imaginary part
  x, y = float(x), float(y)

[[ 957.  949.  968. ... 1032. 1022.  990.]
 [4035. 4025. 4020. ... 4000. 4000. 3920.]
 [ 650.  649.  657. ...  678.  662.  646.]
 ...
 [2138. 2131. 2133. ... 2110. 2105. 2069.]
 [1990. 2000. 1985. ... 1965. 1950. 1930.]
 [1645. 1630. 1645. ... 1670. 1650. 1620.]]
epoch number:  1
Correlation matrix

Eigenvalues:

[[ 994.  963.  933. ...  854.  857.  849.]
 [4050. 4000. 3905. ... 3865. 3870. 3875.]
 [ 661.  641.  632. ...  608.  611.  605.]
 ...
 [2091. 2084. 2067. ... 2168. 2165. 2163.]
 [1995. 2010. 1980. ... 2065. 2055. 2070.]
 [1635. 1645. 1620. ... 1610. 1615. 1620.]]
epoch number:  2
Correlation matrix

Eigenvalues:

[[ 846.          843.          842.         ...  829.
   816.          819.        ]
 [3820.         3845.         3890.         ... 3915.
  3825.         3875.        ]
 [ 598.          586.40002441  590.         ...  580.79998779
   577.59997559  582.20001221]
 ...
 [2161.         2139.         2141.         ... 2130.
  2137.         2138.        ]
 [2025.         2015.         2000.         ... 1955.
  1945.         1940.        ]
 [1600.         1590.         1600.         ... 1575.
  1565.         1570.        ]]
epoch number:  3
Correlation matrix

Eigenvalues:

[[ 856.          878.          822.         ...  815.
   822.          811.        ]
 [3850.         3900.         3860.         ... 3815.
  3815.         3775.        ]
 [ 581.20001221  588.20001221  580.59997559 ...  612.
   605.          602.        ]
 ...
 [2163.         2167.         2154.         ... 1937.
  1957.         1950.        ]
 [1955.         1970.         1960.         ... 1855.
  1865.         1845.        ]
 [1590.         1595.         1585.         ... 1465.
  1495.         1470.        ]]
epoch number:  4
Correlation matrix


#Create the matrix of returns
mat = np.array(df.T[1::].T,float)
mat_ret = returns(mat)

#Number of epochs:
Ne = len(mat_ret[0])//40

epochs = []
for i in range(Ne):
    #Take the ith epoch
    ep = mat_ret[:,i*40:i*40+40]
    epochs.append(ep)


# Plot the heatmap and eigenvalues of each epoch.

for i in range(N):
    ep = epochs[i]
    print(ep)
    
    print("epoch number: ", i)
    
    C= np.corrcoef(ep)
    
    print("Correlation matrix")
    plt.imshow(C,vmin=-1,vmax=1)
    plt.colorbar()
    plt.show()
    
    
    print("Eigenvalues:")
    
    eig = np.linalg.eigvals(C)
    eig_nonzero = [i for i in eig if abs(i) > 0.001]
    a,b,c = plt.hist(eig_nonzero, density = True, bins = 100)
    plt.show()

[[-0.01001001  0.01415571 -0.01894317 ...  0.01737242  0.02561366
  -0.00416233]
 [ 0.00519481  0.          0.01550388 ... -0.00248447  0.00498132
   0.        ]
 [ 0.00864553  0.          0.         ...  0.         -0.02092676
  -0.00763359]
 ...
 [ 0.00188768  0.         -0.00094206 ...  0.00807985  0.00660066
   0.00140515]
 [ 0.0080429  -0.00531915  0.00802139 ...  0.01550388  0.01017812
   0.00251889]
 [ 0.0221519   0.00619195  0.00307692 ...  0.02173913  0.00911854
  -0.00903614]]
epoch number:  0
Correlation matrix

Eigenvalues:

[[-0.00835946  0.02002107  0.0072314  ... -0.00968992 -0.03131115
   0.0040404 ]
 [-0.00247831 -0.00124224  0.00621891 ...  0.         -0.02
   0.03316327]
 [-0.00153846  0.01232666  0.01369863 ... -0.02359882 -0.02416918
   0.02321981]
 ...
 [-0.00327409  0.00093853 -0.00468823 ... -0.00236967 -0.01710214
   0.01063316]
 [ 0.00502513 -0.0075      0.00251889 ... -0.00763359 -0.01025641
   0.03367876]
 [-0.00911854  0.00920245  0.00303951 ... -0.01197605 -0.01818182
   0.00925926]]
epoch number:  1
Correlation matrix

Eigenvalues:

[[-0.03118712 -0.03115265  0.02250804 ...  0.00351288 -0.00933489
  -0.00353357]
 [-0.01234568 -0.02375     0.00128041 ...  0.00129366  0.00129199
  -0.01419355]
 [-0.03025719 -0.01404056  0.00474684 ...  0.00493421 -0.00981997
  -0.01157025]
 ...
 [-0.00334768 -0.00815739  0.01112724 ... -0.00138376 -0.00092379
  -0.00092464]
 [ 0.0075188  -0.01492537 -0.00252525 ... -0.00484262  0.00729927
  -0.02173913]
 [ 0.00611621 -0.01519757  0.00308642 ...  0.00310559  0.00309598
  -0.01234568]]
epoch number:  2
Correlation matrix

Eigenvalues:

[[-0.0035461  -0.00118624  0.01068884 ... -0.01568154  0.00367647
   0.04517705]
 [ 0.0065445   0.01170351  0.         ... -0.02298851  0.0130719
  -0.00645161]
 [-0.01939795  0.00613911  0.         ... -0.00550966  0.00796405
  -0.00171762]
 ...
 [-0.01018047  0.00093502 -0.0032695  ...  0.00328638  0.00046795
   0.01169317]
 [-0.00493827 -0.00744417  0.         ... -0.00511509 -0.00257069
   0.00773196]
 [-0.00625     0.00628931  0.         ... -0.00634921  0.00319489
   0.01273885]]
epoch number:  3
Correlation matrix

Eigenvalues:

[[ 0.02570093 -0.06378132 -0.02189781 ...  0.00858896 -0.013382
  -0.01726264]
 [ 0.01298701 -0.01025641 -0.00129534 ...  0.         -0.01048493
   0.0013245 ]
 [ 0.01204405 -0.01292084  0.0196349  ... -0.01143791 -0.00495868
  -0.00166113]
 ...
 [ 0.00184928 -0.00599908  0.01021356 ...  0.01032525 -0.0035769
   0.00307692]
 [ 0.00767263 -0.00507614  0.01020408 ...  0.00539084 -0.01072386
   0.01084011]
 [ 0.00314465 -0.00626959  0.00630915 ...  0.02047782 -0.01672241
   0.        ]]
epoch number:  4
Correlation matrix

Eigenvalues:


len(mat_ret)

211

	2010-01-04	2010-01-05	2010-01-06	2010-01-07	2010-01-08	2010-01-12	2010-01-13	2010-01-14	2010-01-15	2010-01-18	...	2012-12-14	2012-12-17	2012-12-18	2012-12-19	2012-12-20	2012-12-21	2012-12-25	2012-12-26	2012-12-27	2012-12-28
Ticker
4151.t	999.0	989.0	1003.0	984.0	991.0	984.0	985.0	990.0	989.0	975.0	...	845.0	848.0	852.0	861.0	850.0	852.0	856.0	850.0	851.0	849.0
4502.t	3850.0	3870.0	3870.0	3930.0	3900.0	3940.0	3930.0	3970.0	3970.0	3945.0	...	3805.0	3835.0	3845.0	3870.0	3875.0	3865.0	3865.0	3865.0	3860.0	3855.0
4503.t	694.0	700.0	700.0	700.0	702.0	700.0	696.0	704.0	702.0	697.0	...	797.0	800.0	809.0	812.0	802.0	792.0	797.0	798.0	780.0	775.0
4506.t	979.0	984.0	991.0	982.0	981.0	977.0	979.0	982.0	980.0	965.0	...	999.0	1013.0	1019.0	1026.0	1012.0	1010.0	1021.0	1032.0	1033.0	1035.0
4507.t	2003.0	2007.0	2007.0	1957.0	1930.0	1931.0	1904.0	1968.0	1957.0	1926.0	...	1349.0	1382.0	1443.0	1462.0	1461.0	1457.0	1454.0	1469.0	1479.0	1437.0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
9501.t	2355.0	2375.0	2375.0	2424.0	2441.0	2445.0	2440.0	2484.0	2470.0	2465.0	...	152.0	202.0	237.0	230.0	233.0	224.0	229.0	228.0	220.0	206.0
9502.t	2250.0	2259.0	2259.0	2273.0	2275.0	2286.0	2295.0	2308.0	2310.0	2317.0	...	1084.0	1188.0	1147.0	1159.0	1157.0	1158.0	1177.0	1169.0	1162.0	1150.0
9503.t	2119.0	2123.0	2123.0	2121.0	2131.0	2137.0	2130.0	2139.0	2128.0	2125.0	...	782.0	920.0	879.0	904.0	922.0	956.0	977.0	967.0	952.0	907.0
9531.t	1865.0	1880.0	1870.0	1885.0	1875.0	1875.0	1880.0	1870.0	1870.0	1870.0	...	2015.0	2040.0	2030.0	2035.0	2045.0	2045.0	2030.0	2025.0	2010.0	1975.0
9532.t	1580.0	1615.0	1625.0	1630.0	1625.0	1630.0	1635.0	1635.0	1640.0	1630.0	...	1615.0	1620.0	1595.0	1605.0	1610.0	1605.0	1595.0	1595.0	1580.0	1570.0

Now we do it for the returns¶

Epochs¶

Now we do the same but for the matrix of returns¶